Stability for switched Cohen-Grossberg neural networks with average dwell time
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This paper studies the stability of switched Cohen-Grossberg neural networks with interval time-varying delay and distributed time-varying delay. A piecewise Lyapunov function is utilized to deal with the switching problems of stability. The switching signals are arbitrary under the constraint of the average dwell time which is calculated by collecting the state decay estimation of subsystem. Sufficient conditions are obtained in terms of linear matrix inequality (LMI) to guarantee the exponential stability for the switched Cohen-Grossberg neural networks. Numerical example is provided to illustrate the effectiveness of the proposed method.Keywords:
Dwell time
Linear matrix inequality
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The exponential stability of switched nonlinear cascade systems with time-delay is studied in this paper. By using the average dwell-time method and piecewise Lyapunov function approach, the sufficient conditions that make the switched systems exponentially stable are obtained. And the switching law is designed, which included the average dwell-time of the switched systems. Meanwhile, systems with uncertainties are also considered. The result can be described in the form of LMI, which can be evaluated easily. Finally, a simulation example is given to illustrate the validity of the result.
Dwell time
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Dwell time
Linear matrix inequality
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This paper is concerned with the problem of exponential stability analysis of continuous-time switched delayed neural networks. By using the average dwell time approach together with the piecewise Lyapunov function technique and by combining a novel Lyapunov-Krasovskii functional, which benefits from the delay partitioning method, with the free-weighting matrix technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with constant and time-varying delays, respectively. Moreover, the decay estimates are explicitly given. The results reported in this paper not only depend upon the delay but also depend upon the partitioning, which aims at reducing the conservatism. Numerical examples are presented to demonstrate the usefulness of the derived theoretical results.
Dwell time
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Dwell time
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Linear matrix inequality
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In this paper, some ideas of switched systems with distributed time-varying delays are investigated. Based on the Lyapunov-Krasovskii functional and free-weighting matrices technique, the average dwell time method is applied to ensure the exponential stability of the systems. And a new stability criterion is obtained by the means of linear matrix inequities (LMI). Finally, a numerical example is presented to demonstrate the effectiveness and feasibility of the results obtained.
Dwell time
Matrix (chemical analysis)
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The stability for the switched Cohen‐Grossberg neural networks with mixed time delays and α ‐inverse Hölder activation functions is investigated under the switching rule with the average dwell time property. By applying multiple Lyapunov‐Krasovskii functional approach and linear matrix inequality (LMI) technique, a delay‐dependent sufficient criterion is achieved to ensure such switched neural networks to be globally exponentially stable in terms of LMIs, and the exponential decay estimation is explicitly developed for the states too. Two illustrative examples are given to demonstrate the validity of the theoretical results.
Dwell time
Linear matrix inequality
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